Modifying what vertices a bone affects
Thanks to @leander for this: The way to do this is to first select the object whose bone influences you are looking to modify. You can then go into edit mode and into the object data properties.
From there you can see a list of the bones affecting the object and by clicking on each one you get to see what vertices it has an influence on (the vertex groups of the bone). You can then remove any unwanted influence or assign an influence it doesn't currently have.